- #1
utkarshakash
Gold Member
- 854
- 13
Homework Statement
Number of integral values of m for the equation [itex]\sin x - \sqrt{3} \cos x = \dfrac{4m-6}{4-m}[/itex] to have a solution is
The Attempt at a Solution
I started by plotting the graph of sinx and √3 cosx. Now if I shift the graph of √3 cosx to √3 units above or below its current position I can still have a solution. In other way 4m-6/4-m can be seen as a numerical constant that determines the shift in the graph of √3 cosx. Imposing the inequality
[itex]- \sqrt{3} \leq \dfrac{4m-6}{4-m} \leq \sqrt{3} [/itex]
and solving, I get a different answer.